Surface areas and volumes quantify the size and capacity of three-dimensional objects. They describe how much material covers a solid’s surface and how much space the solid occupies. Using formulas, students calculate surface areas for cubes, cuboids, spheres, cones, and cylinders, and determine volumes for these shapes as well as prisms, pyramids, and hemispheres. These calculations appear in CBSE Class 10 Maths to solve real-world problems such as packaging, construction, and storage. Accurate application of formulas ensures precise results for both theoretical questions and practical scenarios.
In this blog, you will get to know all the important surface area and volume formulas for Class 10 Maths, including their uses and stepwise calculations.
Understanding surface areas and volumes is essential for solving real-world 3D problems. Surface area measures the total material needed to cover a solid, while volume calculates the space it occupies. These calculations are important in construction, packaging, manufacturing, and other practical applications. In Class 10 Maths, formulas simplify these computations for cubes, cuboids, cylinders, cones, spheres, and other solids.
Total surface area of a cuboid with length l, breadth b, and height h= 2(lb + bh + lh)
Lateral surface area of a cuboid= 2(l + b)h
Surface area of a cube (edge length l)= 6l²
Lateral surface area of a cube (edge length l)= 4l²
Volume of a cube= l³
Curved surface area of a cylinder with radius r and height h = 2πrh
Total surface area of a cylinder= 2πr(h + r)
Volume of a cylinder= πr²h
Curved surface area of a cone with radius r and slant height L= πrL
Total surface area of a cone= πr(L + r)
Volume of a cone= ⅓πr²h
Surface area of a sphere= 4πr²
Volume of a sphere= 4⁄3πr³
Volume of a frustum of a cone with radii r₁, r₂ and height h= ⅓πh(r₁² + r₂² + r₁r₂)
| Figure | Perimeter / Base Formula | Total Surface Area (TSA) | Lateral / Curved Surface Area (LSA/CSA) | Volume (V) |
| Square | 4 × side | side² × 6 (if cube considered) | – | |
| Rectangle | 2(l + b) | 2(l × b + b × h + l × h) | – | |
| Parallelogram | 2(a + b) | b × h | – | |
| Trapezoid | a + b + c + d | ½ × (a + b) × h | – | |
| Triangle | a + b + c | ½ × base × height | – | |
| Circle | 2πr | πr² | – | |
| Ellipse | 2π√((a² + b²)/2) | π × a × b | – | |
| Cuboid | 4(l + b + h) | 2(lb + bh + hl) | 2h(l + b) | l × b × h |
| Cube | 12 × a | 6a² | 4a² | a³ |
| Cylinder | – | 2πr(h + r) | 2πr × h | πr² × h |
| Cone | – | πr(l + r) | πr × l | (1/3)πr²h |
| Sphere | – | 4πr² | 4πr² | (4/3)πr³ |
| Hemisphere | – | 3πr² | 2πr² | (2/3)πr³ |
| Right Pyramid | – | Base area + ½ × perimeter × slant height | ½ × perimeter × slant height | (1/3) × Base area × height |
| Right Circular Frustum of Cone | – | π(R + r)l + π(R² + r²) | π(R + r)l | (1/3)πh(R² + r² + Rr) |
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